Two Pendula on 70cm Strings Collision Angle

[Sean77771]

Homework Statement

Two pendula are suspended on 70cm strings connected at the same point on a ceiling. The mass on the left is 45g and is held so the string makes an angle of 10 degrees with the vertical. The mass on the right is 65g and is held in the opposite direction so the string makes an angle of 4.2 degrees with the vertical. When the masses are released, what is the value of the angle where they collide?

Homework Equations

Pendula equations

The Attempt at a Solution

I have no idea how to figure this out. I am pretty sure that the periods of the pendula are independent of their masses, which would lead me to believe that they would collide at an angle of 0 (right on the vertical) but I don't know how to prove this.

 

[catkin]

I agree. Even using the more accurate formula for larger amplitudes(http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.html#c1) the error of the simple formula for the 10 degree pendulum is less than 0.2%

 

[ogb p]

I would approach this problem by first setting up the equations for the two pendula. The period of a pendulum is given by T = 2π√(L/g), where L is the length of the string and g is the acceleration due to gravity. In this case, both pendula have the same length of 70cm, but different masses. Therefore, their periods will be different.

Next, I would consider the initial conditions of the masses. The left mass is held at an angle of 10 degrees, while the right mass is held at an angle of 4.2 degrees. This means that when released, the left mass will have a velocity component in the horizontal direction, while the right mass will have a velocity component in the vertical direction.

To find the angle at which they collide, I would need to consider the motion of the masses in both the horizontal and vertical directions. This can be done by setting up equations for the position, velocity, and acceleration of each mass at any given time. By solving these equations simultaneously, I can determine the point at which the masses will collide.

It is important to note that the collision angle may not be exactly 0 degrees, as there will be some slight deviation due to factors such as air resistance and friction. However, it can be assumed that the angle will be very close to 0 degrees.

In conclusion, as a scientist, I would use mathematical equations and principles to determine the angle at which the two pendula will collide. This would involve considering the initial conditions and motion of the masses, and solving equations to find the point of collision.